An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable breaks when the elevator is at a height h above the top of the spring, calculate the value that the spring constant k should have so that passengers undergo an acceleration of no more than 7.0 g when brought to rest. Let M be the total mass of the elevator and passengers. Express your answer in terms of the variables h, M, and appropriate constants.
k = ?

Explanation:

Acceleration will be in upward direction due to force by spring in upward direction .Let maximum compression be x .

maximum force  = k x -Mg

k x - Mg = 7Mg

kx = 8Mg

After falling by height h , compression in spring is x

1/2 k x² = Mg( h + x )

1/2 x 8Mg x = Mgh +Mgx

4Mgx = Mgh +Mgx

3 Mgx = Mgh

x = h / 3

kx = 8Mg

k h/3 = 8Mg

k = 24 Mg / h

i think it’s a. this is because if they measured the mass of something with a mass of 150g, then their final answer would have to be approximately 150g. though all of their answers are almost 150, rosa and tran have the closest answers (or the exact answer) to the accurate one.

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